K3 metrics

2020/06/03 by Kachru, Shamit, Tripathy, Arnav, Zimet, Max
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2006.02435

Abstract

We provide an explicit construction of Ricci-flat K3 metrics. It employs the technology of D-geometry, which in the case of interest is equivalent to a hyper-Kähler quotient. We relate it to the construction of arXiv:1810.10540, and in particular show that it contains the solution to the BPS state counting problem (that of computing the BPS index of a heterotic little string theory compactified on T²) discussed therein, which is the data needed for this second construction of K3 metrics.

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